If the lengths of a pair of opposite sides of a square were tripled and the other pair were each increased by 7 cm,the new figure would be rectangle with a perimeter 96 cm find the dimensions of the original square
original dimensions s x s
new dimensions; 3s x (s+7)
perimeter new=96=6s+2s+14
8s=82
s=82/8
The square on the hypotenuse
Let's solve this problem step by step:
1. Let's assume the original side length of the square is "x" cm.
So, the original dimensions of the square are x cm x x cm.
2. According to the given information:
- The lengths of a pair of opposite sides of the square were tripled.
So, the new dimensions for these sides are 3x cm x 3x cm.
- The other pair of sides were each increased by 7 cm.
So, the new dimensions for these sides are (x + 7) cm x (x + 7) cm.
3. The new figure is a rectangle with dimensions:
Length = 3x cm
Width = x + 7 cm
4. The perimeter of a rectangle is given by the formula: P = 2(Length + Width).
5. Substituting the given values, the new rectangle's perimeter is:
96 cm = 2[(3x + x + 7) cm]
6. Simplifying the equation:
48 cm = 4x + 7 cm
7. Rearranging and solving for x:
4x = 48 cm - 7 cm
4x = 41 cm
x = 41 cm / 4
x = 10.25 cm
Therefore, the original square has sides measuring approximately 10.25 cm.